Polygonal mirror optical scanning system

ABSTRACT

An optical system for scanning a light beam across an object where the light beam is double reflected by the reflection surfaces of a rotating polygonal mirror. Beam expander optics are included in the light path for the light beam following the first reflection by the polygonal mirror to magnify the beam diameter to fill the length of the reflective surface of the polygonal mirror at the second reflection. The beam expander optics further include lenses for demagnifying scan angle in the light beam following the first reflection. The lenses of the beam expander optics are formed with a Petzval curvature (third order Seidel aberration) to correct for the distortion induced in the optics image plane by the longitudinal shift in the entrance pupil position at the first reflection as the polygonal mirror rotates.

This is a division of application Ser. No. 08/330,834 filed on Oct. 27,1994, now U.S. Pat. No. 5,585,955, which is a division of applicationSer. No. 07/963,549 filed Oct. 20, 1992, now U.S. Pat. No. 5,392,149,granted on Feb. 21, 1995.

TECHNICAL FIELD

The present invention relates to optical scanning systems and, inparticular, to an optical scanning system wherein a beam of light isreflected by the reflective surfaces of a rotating polygonal mirror toscan across an object.

BACKGROUND OF THE INVENTION

It is common in scanning optical systems used for reading and recordinginformation to employ a rotating polygonal mirror as a light reflector.The polygonal mirror typically comprises a plurality of precisely angledreflecting surfaces (facets) assembled about an axis in an equilateralpolygon configuration. Rotation of the polygonal mirror about its axiswill cause a light beam incident thereon to be sequentially reflected byeach of the facets and repetitively swept with each reflection through apredetermined arc. Optics in the form of lenses and reflectors may alsobe included in the system to direct the swept beam to scan across thesurface of an object.

It is also known to reflect the repetitively swept beam back to therotating polygonal mirror where the beam is again sequentially reflectedby each of the facets and repetitively swept through anotherpredetermined arc. Additional optics may then be utilized to receive andfocus the swept beam for scanning of the surface of the object. In sucha system, the included optics are further employed to shape the sweptbeams generated by both the first and second polygonal mirrorreflections such that the beam swept by the first reflection by thepolygon is expanded to track the rotational movement of the polygonfacets at the second reflection. U.S. Pat. Nos. 4,624,528; 4,129,355;4,030,806 and 3,972,583 are illustrative of the use of a doublereflecting scanner system and included optics.

Due to the nature of the rotating polygonal mirror, the point on eachreflective surface (facet) of the polygonal mirror where reflection ofthe light beam occurs is longitudinally shifted with respect to thelight path of the incident beam as the polygonal mirror rotates and thereflected beam is swept through the predetermined arc. If optics areincluded in the system for receiving the swept beam reflected by therotating polygonal mirror, the entrance pupil for the included opticswill also be shifted, in a manner corresponding to the point on thereflective surface, as the polygonal mirror rotates. The shifting (ordistortion) of the position of the entrance pupil caused by the rotationof the polygonal mirror results in a field curvature at the image planeof the included optics that adversely distorts the swept beam.

SUMMARY OF THE INVENTION

The optical scanning system of the present invention comprises arotating mirror for generating a repetitively swept beam and beamexpander optics to generate a scanning beam therefrom. The opticsinclude an eyepiece lens having a negative Petzval curvature(aberration) for inducing an inward field curvature in the image planeof the eyepiece lens to correct for the distortion induced in the sweptbeam by the shifting position of the entrance pupil resulting fromrotation of the mirror. The Petzval curvature comprises a third orderaberration and is the fourth aberration term of the Seidel aberrationpolynomial. The generated distortion corrected, swept scanning beam isthen focused and scanned across the surface of an object.

In another embodiment of the system, the distortion corrected swept beamis expanded and collimated by an objective lens of the beam expanderoptics into a scan beam having a diameter substantially equal to thelength of each facet of the rotating mirror. The expanded scan beam isthen reflected back to the rotating mirror to track the rotationalmovement of each facet therein and be reflected thereby, with thereflected scan beam sweeping an arc to scan across the surface of theobject.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention may be had byreference to the following Detailed Description when taken inconjunction with the accompanying Drawings wherein:

FIG. 1A is a schematic diagram showing one embodiment of the scanningoptical system of the present invention;

FIG. 1B shows an alternative positioning of the light beam and rotatingpolygonal mirror illustrated in the system of FIG. 1A;

FIGS. 2A, 2B and 2C illustrate in detail the reflecting of the incidentbeam by the reflective surfaces of the rotating polygonal mirror shownin FIG. 1B and the longitudinal shifting of the entrance pupil due torotation of the polygonal mirror;

FIG. 3 is a graph showing the field curvature induced by thelongitudinal shift in the entrance pupil position as the polygonalmirror rotates;

FIG. 4 is a graph showing the field curvature for the swept beamfollowing correction by the Petzval curvature of the beam expandereyepiece lens;

FIG. 5 is a schematic diagram showing another embodiment of the scanningoptical system of the present invention; and

FIG. 6 is a schematic diagram showing another embodiment of the scanningoptical system of the present invention.

DETAILED DESCRIPTION OF THE DRAWINGS

Reference is now made to FIGS. 1A and 1B wherein there is illustratedthe scanning optical system 10 of the present invention. A collimatedlight beam 12 emitted from a source 14 is directed to a polygonal mirror16 comprised of a plurality of precisely angled reflective surfaces (orfacets) 18 assembled about an axis 20 in an equilateral polygonconfiguration. A motor 22 having a shaft (not shown) mounted to thepolygonal mirror 16 at the axis 20 thereof causes the polygonal mirrorto rotate about the axis in the direction indicated by the arrow 24.

With rotation of the polygonal mirror 16, the inclination (or angle) ofeach reflective surface 18 with respect to the position of the lightbeam 12 changes from a starting inclination angle 26 through a centerinclination angle 28 to an ending inclination angle 30. In FIG. 1A, thelight beam 12 is directed at the polygonal mirror 16 but is offset fromthe axis 20. Conversely, in FIG. 1B, the light beam 12 is aimed directlyat the axis 20 of the polygonal mirror 16. In the latter orientation(FIG. 1B), the incident light beam 12 will be orthogonal to thereflective surface 18 at the center inclination angle 28. As thepolygonal mirror 16 continues to rotate about the axis 20, thereflective surface 18 moves away from the light beam 12 (following theending angle 30) and the next reflective surface on the polygonal mirrormoves into position (at the starting angle 26) to reflect the lightbeam.

The rotation of the polygonal mirror 16 and movement of a reflectivesurface 18 from the starting through ending inclination angles (26through 28 to 30) causes the light beam 12 to be reflected and generatea reflected beam 32 that is swept by the rotation of the polygonalmirror through a predetermined arc 34 (in the direction indicated by thearrow head 36). The reflected light beam 32 sweeps through the arc 34from a starting sweep position 38 through a center sweep position 40 toan ending sweep position 42 corresponding to the starting, center andending inclination angles 26, 28 and 30, respectively, for thereflective surface 18. With continued rotation of the polygonal mirror16 about the axis 20, subsequent reflective surfaces 18 sequentiallymove into position to reflect the light beam 12 causing the reflectedlight beam 32 to be repetitively swept through the arc 34.

The optical system 10 further includes beam expander optics 44comprising an eyepiece lens 46 and an objective lens 48. It will, ofcourse, be understood that the eyepiece lens 46 and objective lens 48may each include a plurality of lenses and that the single lenses shownfor each in FIG. 1A are illustrative only. The beam expander optics 44are optically positioned in the swept light path of the reflected lightbeam 32 such that the eyepiece lens 46 focuses the reflected beam andthe objective lens 48 expands and collimates the reflected beam togenerate a scanning beam 50. In particular, the beam expander optics 44function to demagnify the sweep angle of the reflected light beam 32associated with the arc 34 to repetitively project the scanning beam 50through an arc 59 across the surface of an object 58 in the directionindicated by the arrow head 60 from a starting scan position 52 througha center scan position 54 to an ending scan position 56 (that correspondto the starting, center and ending sweep positions, 38, 40 and 42,respectively). It should be noted that the nature of the beam expanderoptics 44 reverses the image of the swept beam 32 such that thedirection 60 of the sweep of the scanning beam 50 is opposite than thedirection 36 of the swept beam 32. The beam expander optics 44 furtherfunction to magnify the diameter of the scanning beam 50 projected onthe object 58 or alternatively focus the scanning beam to a spot on thesurface of the object if desired.

Referring now to FIGS. 2A, 2B and 2C, there are shown a series ofillustrations detailing the reflection of the incident light beam 12,having, by the orientation shown in FIG. 1B, the reflective surfaces 18of the rotating polygonal mirror 16. FIG. 2A illustrates such reflectionwhen the reflective surface 18 is at the starting angle 26. FIG. 2Billustrates such reflection when the reflective surface 18 is at thecenter angle 28 and orthogonal to the light beam 12. FIG. 2C illustratessuch reflection when the reflective surface 18 is at the ending angle30. It will, of course, be understood that the dimensions illustrated inFIGS. 2A, 2B and 2C are exaggerated to facilitate a more completeunderstanding of the reflection process.

An entrance pupil 62 for the eyepiece lens 46 that focuses the reflectedlight beam 32 is projected on the reflective surface 18 of the polygonalmirror at the point where the light beam 12 is reflected. Rotation ofthe polygonal mirror 16 such that the reflective surface 18 moves fromthe starting angle 26 through the center angle 28 to the ending angle 30causes the position of the entrance pupil 62 to shift as shown at 64 inlongitudinal relation to the light path for the light beam 12. Theshifting of the position of the entrance pupil 62 due to rotation of thepolygonal mirror 16 causes field curvature in the image plane 66 (FIGS.1A and 1B) of the a focal eyepiece lens 46 that adversely distorts thereflected light beam 32. The amount (x) of longitudinal shift 64 (andhence the induced distortion in the image plane) is determined by thedimensions of the polygonal mirror 16 according to the followingequation:

    x= R/cos(α)!-R                                       (1)

wherein:

    R=minor axis length 93 (FIG. 1A),=L/ 2*tan(π/N)!,       (2)

    N=number of reflective surfaces,

    L=reflective surface length 94 (FIG. 1A),                  (3)

    d=light beam 12 diameter, and

    α=useful scan angle=(π/N)-arctan  d/(2*R)!.       (4)

The amount of longitudinal shift 64 (corresponding to the induced fieldcurvature at the image plane 66) varies as a function of the rotation ofthe polygonal mirror 16 according to the following equation based onequation (1):

    x.sub.i = R/cos(α.sub.i)!-R                          (5)

wherein:

i=0 through 10, and

    α.sub.i (α*i)/10.

To correct for the distortion induced in the reflected light beam 32 bythe longitudinal shift 64 in the position of the entrance pupil 62, theeyepiece lens 46 is modified by adding a Petzval curvature (a thirdorder Seidel aberration) thereto. The Petzval curvature (p) for theeyepiece lens 46 is given according to the following equation:

    p=(-1/2)* h.sup.2 /(f*n)!                                  (6)

wherein:

    h=f*tan(α),                                          (7)

    n=refractive index, and

    f=eyepiece lens 46 focal length.

Substituting equation (7) into equation (6) yields:

    p=(-1/2)* (f*tan(α).sup.2)/n!.                       (8)

Solving for the afocal eyepiece lens 46 focal length (f) yields:

    f=-2*p*n/tan(α).sup.2                                (9)

If the longitudinal pupil shift (x) from equation (1) is assumed to beequal to the desired Petzval curvature (p) (to cancel out the distortioninduced by the longitudinal shift), then equation (9) yields:

    f=2*x*n/tan(α).sup.2.                                (10)

The amount of Petzval curvature (p) should vary as a function of therotation of the polygonal mirror 16 to substantially cancel thedistortion induced by the longitudinal shift in the entrance pupilaccording to the following equation based on equation (8):

    p.sub.i =(-1/2)* (f*tan(α.sub.i).sup.2)/n!           (11)

wherein:

f is determined from equation (10). The effective distortion due tolongitudinal shift (corresponding to the corrected field curvature atthe image plane 66) is determined according to the following equationbased on equations (5) and (11):

    x.sub.i =x.sub.i +p.sub.i                                  (12)

wherein:

i=0 through 10.

For a more complete understanding of the effectiveness of the Petzvalcurvature for correcting the entrance pupil 56 distortion caused by thelongitudinal pupil shift 64, consider the following example wherein:

d=1 mm,

L=100 mm,

N=15, and

n=1.51.

According to equation (1), the longitudinal pupil shift 64 (x) is equalto 5.147 millimeters. A graph showing the variation in the amount ofinduced field curvature according to equation (5) as the polygonalmirror 16 rotates is shown in FIG. 3 with the calculated values of x_(i)shown in column 3 of Table 1. To correct for the 5.147 millimeterdistortion, the Petzval curvature requires a focal length (f) accordingto equation (10) of 351.356 millimeters. The calculated values of thePetzval curvature p_(i) according to equation (11) are shown in column 4of Table 1. A graph showing the effective induced field curvature(x_(i)) following correction of the longitudinal pupil shift by thePetzval curvature according to equation (12) is shown in FIG. 4 with thecalculated values of x_(i) according to equation (12) shown in column 5of Table 1. FIGS. 3 and 4 and Table 1 illustrate that approximatelyninety-nine percent of the induced field curvature (x_(i)) in thisexample is eliminated (x_(i)) through cancellation by the includedPetzval aberration (p_(i)).

                  TABLE 1                                                         ______________________________________                                                α.sub.i                                                                          x.sub.i    p.sub.i x.sub.i                                   i       (radians)                                                                              (mm)       (mm)    (mm)                                      ______________________________________                                        0       .000000  .000000    .000000 .000000                                   1       .020732  .050587    -.050020                                                                              .000567                                   2       .041463  .202238    -.200244                                                                              .001994                                   3       .062194  .455584    -.451189                                                                              .004395                                   4       .082926  .811044    -.803741                                                                              .007303                                   5       .103657  1.269540   -1.259089                                                                             .010451                                   6       .124389  1.831553   -1.818865                                                                             .012688                                   7       .145120  2.498788   -2.484978                                                                             .013810                                   8       .165852  3.272762   -3.259849                                                                             .012913                                   9       .186583  4.154797   -4.146166                                                                             .008631                                   10      .207315  5.147241   -5.147212                                                                             .000029                                   ______________________________________                                    

Referring now to FIG. 5, there is shown another embodiment of thescanning optical system 10' of the present invention wherein thescanning light beam 50 is directed back toward the rotating polygonalmirror 16 by a pair of reflecting mirrors 68. Movement of the scanninglight beam 50 from the starting scan position 52 through the center scanposition 54 to the ending scan position 56 tracks and corresponds withthe inclination movement of a reflective surface 18' on the polygonalmirror 16 from a starting, center and ending angles 26', 28' and 30',respectively. As mentioned earlier, the beam expander optics 44 functionto magnify the diameter of the projected scanning beam 50 and decreasethe scanning angle arc. Preferably, the diameter of the scanning beam ismagnified to be substantially equal to the length of the reflectivesurface 18'.

Movement of the reflective surface 18' due to rotation of the polygonalmirror 16 causes the scanning beam 50 to be reflected and generate asecondary reflected beam 70 that is swept by the rotation of thepolygonal mirror through an arc 72 (in the direction indicated by thearrow head 74). The secondary reflected light beam 70 sweeps through thearc 72 from a starting secondary sweep position 76 through a centersecondary sweep position 78 to an ending secondary sweep position 80corresponding to the starting, center and ending angles 26', 28' and30', respectively, for the reflective surface 18'. With continuedrotation of the polygonal mirror 16 about the axis 20, subsequentreflective surfaces 18' move into position to reflect the scanning beam50 causing the secondary reflected light beam 70 to be repetitivelyswept through the arc 72.

The optical system 10' further includes focusing optics 82 comprising afocusing lens 84. It will, of course, be understood that the focusinglens 84 may include a plurality of lenses and that the single lens shownin FIG. 5 is illustrative only. It will, of course, further beunderstood that focusing optics 82 may not be required in everyapplication of the system 10'. The focusing optics 82 are opticallypositioned in the light path of the secondary reflected light beam 70 togenerate a secondary scanning beam 86 such that the focusing lens 84focuses the secondary reflected beam to a spot on the surface of theobject 58. The focusing optics 82 further function to project thesecondary scanning beam 86 from a starting secondary scan position 88through a center secondary scan position 90 to an ending secondary scanposition 92 (that correspond with the starting, center and endingsecondary sweep positions, 76, 78 and 80, respectively) parallel to eachother to repetitively scan across the surface of the object 58 in thedirection indicated by the arrow 94.

The embodiments disclosed above utilize a single rotating polygonalmirror 16 in either a single reflection (FIGS. 1A and 1B) or doublereflection (FIG. 5) operation. It will, of course, be understood thattwo separate rotating polygonal mirrors 16 and 16' having correspondingreflective surfaces 18 and 18' therein as in FIG. 6, may be provided inanother embodiment of the scanning optical system 10" for doublereflection operation. The reflective surfaces 18 of the first polygonalmirror 16 need not be the same size as the reflective surfaces 18' ofthe second polygonal mirror 16' provided the relative rates of rotationof the polygonal mirrors are adjusted to account for the differentreflective surface sizes and the magnification of the beam expanderoptics is adjusted to properly size the diameter of the scanning beam 50incident on the second polygonal mirror. Synchronization and adjustmentof the rotation of the polygonal mirrors 16 and 16' is provided by thesynch means 96 coupled to the motors 22 and 22' of each polygonalmirror.

Although several embodiments of the scanning optical system of thepresent invention have been illustrated in the accompanying Drawings anddescribed in the foregoing Detailed Description, it will be understoodthat the invention is not limited to the embodiments disclosed but iscapable of numerous rearrangements and modifications of parts andelements without departing from the scope of the invention.

We claim:
 1. An optical system for scanning a light beam across anobject, comprising:a multi-sided mirror disposed in the path of thelight beam, the mirror having a plurality of reflective surfaces; drivemeans for rotating the mirror in a predetermined direction such that theplurality of reflective surfaces sequentially reflect the light beam togenerate a reflected light beam swept repetitively in a single directionthrough a predetermined arc; and lens means for optically receiving thereflected light beam to project a scanning light beam repetitivelyacross the surface of the object, the lens means having an entrancepupil optically positioned substantially coincident with the reflectivesurface, the entrance pupil subject to longitudinal shifting due to therotation of the polygonal mirror, such longitudinal shifting inducing afield curvature in an image plane distorting the reflected light beam,said lens means comprising an eyepiece lens including a Petzvalcurvature for inducing a field curvature in the image plane to correctfor the entrance pupil shifting in the longitudinal direction inrelation to the path of the scanning light beam and focusing the lightbeam, said lens means further comprising an objective lens formagnifying and collimating the focused light beam, said objective lensbeing located next to the eyepiece lens.
 2. The optical system as inclaim 1 wherein the lens means includes means for demagnifying a scanangle for the predetermined arc swept by the reflected light beam. 3.The optical system as in claim 1 wherein the lens means projects thescanning light beam to move repetitively in a second direction oppositeof said first direction.
 4. An optical system for scanning a light beamacross an object, comprising:a multisided mirror having a plurality ofreflective surfaces rotated in a predetermined direction and disposed inthe path of the light beam to generate a reflected light beam sweptrepetitively by the rotation of the multisided mirror through apredetermined arc; and lens means optically positioned in the path ofthe reflected light beam to generate a scanning light beam for scanningthe surface of the object, the lens means having an entrance pupilsubstantially coincident with a surface of the mirror and having animage plane, the lens means including an eyepiece lens having a thirdorder Seidel aberration varying as a function of the reflective surfacerotation to induce a field curvature in the image plane of the lensmeans to substantially cancel distortion in the image plane induced by alongitudinal shift of the position of the entrance pupil due to rotationof the multisided mirror.
 5. An optical system for scanning a light beamacross an object, comprising:a multisided mirror having a plurality ofreflective surfaces rotated in a predetermined direction and disposed inthe path of the light beam to generate a reflected light beam sweptrepetitively by the rotation of the multisided mirror through apredetermined arc; and lens means optically positioned in the path ofthe reflected light beam to generate a scanning light beam for scanningthe surface of the object, the lens means having an entrance pupilsubstantially coincident with a surface of the mirror and having animage plane, the lens means including an eye piece lens having a Petzvalcurvature varying as a function of the reflective surface rotation toinduce a field curvature in the image plane to substantially canceldistortion in the image plane induced by a longitudinal shift in theposition of the entrance pupil due to rotation of the multisided mirror.6. The optical system of claim 5, wherein the lens means includes meansfor demagnifying a scan angle for the predetermined arc swept by thereflected light beam.
 7. The optical system as in claim 5, wherein thelens means includes means for magnifying and collimating the projectedscanning light beam.